{
 "metadata": {
  "name": "OptimizationDemo1"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Optimization demo\n",
      "=================\n",
      "\n",
      "SciPy's optimization package is scipy.optimize. The most basic\n",
      "non-linear optimization functions are: \n",
      "\n",
      "    * optimize.fmin(func, x0), which finds the minimum of func(x) starting x with x0 (x can be a vector)\n",
      "    * optimize.fsolve(func, x0), which finds a solution to func(x) = 0 starting with x = x0 (x can be a vector) \n",
      "    * optimize.fminbound(func, x1, x2), which finds the minimum of a scalar function func(x) for the range [x1,x2] (x1,x2 must be a scalar and func(x) must return a scalar) \n",
      "\n",
      "See the [scipy.optimze documentation](http://docs.scipy.org/doc/scipy/reference/optimize.html) for details.\n",
      "\n",
      "This is a quick demonstration of generating data from several Bessel\n",
      "functions and finding some local maxima using fminbound. This uses ipython with the -pylab switch."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import optimize, special\n",
      "from numpy import *\n",
      "from pylab import *\n",
      "\n",
      "x = arange(0,10,0.01)\n",
      "\n",
      "for k in arange(0.5,5.5):\n",
      "     y = special.jv(k,x)\n",
      "     plot(x,y)\n",
      "     f = lambda x: -special.jv(k,x)\n",
      "     x_max = optimize.fminbound(f,0,6)\n",
      "     plot([x_max], [special.jv(k,x_max)],'ro')\n",
      "\n",
      "title('Different Bessel functions and their local maxima')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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r4mx+/37UP3MRR+aOwJRbq3QqZq8RtWqJVePDw4HmzUWXzx9/6Lzg+2D/wHdn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      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}